A SPIRIT OF INQUIRY

A Review of David Hackett Fischer’s African Founders

By John Wilson

now—more than thirty years after the appearance of Albion’s Seed—it has come to fruition with the publication of African Founders: How Enslaved Peoples Expanded American Ideals

And here the demands of the present insistently assert themselves, in a way that was not the case for Albion’s Seed. Although more than 150 years have passed since the Emancipation Proclamation, the legacy of slavery and the scandal of ongoing discrimination against black Americans is being studied, protested, and proclaimed with greater intensity than at any point since the Civil Rights movement of the 1950s and early 1960s, perhaps even exceeding it.

I read African Founders with a sort of double-consciousness: on the one hand, absorbed and at many points exhilarated by the extraordinarily wide-ranging findings that Fischer has assembled; on the other hand, thinking about how his book will be perceived and judged (and misjudged) at this present moment. The subtitle of the new book alone will inflame many readers who misconstrue it before they’ve even bothered to read a page. So “Enslaved People Expanded American Ideals,” huh? Very inspiring. And just what we need in 2023: a feel-good narrative. Right.

In fact, Fischer doesn’t at all minimize the evil of slavery and its long aftermath, down to the present day. What he does is quite different: he opens our eyes to the many strands of African influence that the slaves brought with them and transmitted to their descendants (see for example pp. 454—55, on Michelle Obama’s roots, under the heading “A Gullah Heritage in the White House”). I can’t imagine anyone with a genuine interest in American history reading this book without profit, not to mention moments of revelation and delight.

What African Founders doesn’t offer is a continuous narrative. It’s organized by region (the brief section on Michelle Obama’s family comes from a chapter entitled “Coastal Carolina, Georgia, and Florida”) and I read it in discrete chunks, not too much at a session.

The nature of the project is suggested in the introduction, in which Fischer harks back to Herodotus and the spirit of “inquiry” that animated his pioneering work:

In the school of Herodotus, history was not primarily a story, or an argument, or a thesis, or a polemic. In actual practice it sometimes became any or all of those things. But it tended to begin in another way, as an inquiry with a genuinely open end. It started not with answers but with questions, about events that actually happened.

This spirit animates Fischer’s entire enterprise. As he notes, “In our own twenty-first century, these ancient ideas of open inquiry and empirical truth have gained a new importance, in part because of hostile assaults upon them from many directions.”

African Founders is the product of decades of “inquiry,” drawing on an immense range of scholarship as well as on firsthand investigation. I’ve already talked about the book with several serious homeschooling parents, urging them to read it and adapt parts of it for their “curriculum.” I hope you’ll consider giving it a look, too.

One final note. John J. Miller interviewed Fischer about African Founders recently on his podcast The Bookmonger. The interview is short, about eleven minutes, and I recommend it. Near the end, Miller asks Fischer how long he had been working on the book. Fischer says, “All my life,” and goes on to explain that his father was head of the Baltimore public schools at the time of the landmark Supreme Court ruling that mandated desegregation. Seeing his father committing himself to that goal, against outright resistance, foot-dragging, and more, was an experience that fundamentally shaped Fischer’s own sense of what it meant to be an American. Hence, many years later, African Founders

John Wilson edited Books & Culture (1995-2016). He writes regularly for First Things and a range of other magazines. He is a contributing editor at the Englewood Review of Books and senior editor at Marginalia Review of Books.

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s I prepare to teach the book Home by Marilynne Robinson for the fourth time next week to college seniors, I find myself contemplating the provision and pain of home and wondering about Robinson’s vision of the heroic. Home is one of two books (the other is The Idiot by Dostoevsky) I’m not sure I can read ever again because of the acute misery they narrate. My method of teaching requires me to reread the book and to converse anew from inside of the corporeal tissue of the words, images, and sentences each time. I need to reacquaint myself with the particulars as well as the special atmosphere of the living document. Home poses a conflict for me I’m not sure I can overcome this year.

The dramatic stage of this story is small with three central characters: Reverend Robert Boughton, Glory Boughton, and Jack Boughton. The father, Robert, is dying and his children have come home in various degrees of disgrace. Glory is thirty-eight and fresh from a failed romance with a man who was really taking financial advantage of her deep desire to be married and a mother. Jack is forty-three and has been away from home for twenty years, during which time he missed his mother’s fatal illness and funeral, although he took the money his dad sent for him to return—and he intended to return, even bought a suit for the occasion. Reverend Boughton is seventy-four but very weak and losing some of the velvet patience and hope he maintained in his relationship with his prodigal son over four decades of co-suffering. At one point in Gilead (the Pulitzer Prize–winning book in the tetralogy that precedes Home and tells an adjacent story), Robinson calls each person a civilization saying they are “built on the ruins of a number of preceding civilizations but with our own notions of what is beautiful and what is acceptable—which, I hasten to add, we generally do not satisfy and by which we struggle to live” (Gilead, 197).

I happen to have had the privilege of visiting ruins that reveal such historic layers and to have loved Pope Gregory’s instructions to the Roman Christians that they ought to build on top of former pagan temples (St. Clement or Santa Maria Sopra Minerva) or even repurpose them (Pantheon), and I (and others) have taken this up as a metaphor for the relationship between the classical and Christian world, knowledge, and texts. Nonetheless, literally going to one of these churches and taking the remarkable climb downward into the dank underground and seeing the layers of civilization (and cultic activity) is illuminating—second-century mithraeum at the bottom where the underground streams are, fourth-century altar and icons at the musty middle level, eleventh-century church on the top, all within sight of the Colosseum, where some of the most unspeakable atrocities happened against our Christian brothers and sisters. Robinson says by her metaphor that each person contains such layers or stories: foundations, altars, underground streams within our persons. A home is composed of persons trying to make a little city as well governed and flourishing as we can manage. It turns out that even the best of us struggle because at the center of the structure is the mystery of being bound to each other’s suffering (and strangeness). We see in Glory and Jack the edifice that they construct on top of the nave of their father. This presents a good metaphor for what writers do with old texts, and Robinson herself has discretely rewritten the great epics in a narrative about a small town and the life of one family.

I want to reassure you that, according to Robinson, the only thing worse than family life is not having one. Robinson shows us the darkness of loneliness and of not being taken into a family. Pastor John Ames (Boughton’s best friend and Jack’s godfather and namesake), who early lost his wife and child and in his old age (late sixties) meets and marries Lila, says this in Gilead: “My own dark time, as I call it, the time of my loneliness, was most of my life, as I have said, and I can’t make any real account of myself without speaking of it” (44). Lila and John have a son who is seven at the time of his writing the letters that make up the contents of Gilead. They are addressed to the beloved who will grow up without his presence. It is one of the central tasks of his end of life to reconcile himself to sending Lila and Robbie out into the wilderness after his death. Another alternative to family life is Lila’s experience of deadbeat parents who neglect her until she is embraced and “stolen” by Doll, a mother-substitute, who occupies the central place in Lila’s deep heart’s core. By this we understand that Robinson is not some anti-family prophet; she understands Tocqueville’s idea that democracy, like family, is the best of the worst options available. With Aquinas, she also understands that being is itself good from the onset and love is woven into it: “When you love someone to the degree you love her, you see her as God sees her, and that is an instruction in the nature of God and humankind and of Being itself” (Gilead, 139). Robinson shows the most broken people delighting in being, and all her characters have the capacity to enjoy the pleasure of the material world—down to its fundamental element, water. Water is the natural form that baptism participates in and supernaturally completes. Sacrament and nature are the same stuff.

But I was talking about family, and I haven’t yet given you a single quote from the book Home. Jack comes home to be with his father and to sound the city of Gilead where he grew up, to see if there is balm there, to see if he and his African American wife and their son could live in such a place. No one knows this for a long piece of the book. What people know is that he is a prodigal who has, like Odysseus, been away for twenty years. Wait, why are we talking about the Odyssey? Because, like Odysseus, Jack goes home, and when he arrives his father is almost dead and his sister, whose name is Glory, shows him the most profound understanding and acceptance I have ever read.

I’m going to make a bold claim (that I have never read in the critical work or heard the author say). Robinson is rewriting the ancient epics in these books. She is putting her own proud American boast right up there with Homer, but it is a deeply Christian claim. Glory and homecoming are (as Lewis claims in his essay “The Weight of Glory”) recast from the ancient terms (in which the hero accomplishes great deeds that are song-worthy) into taking up the burden of my neighbor’s glory, my neighbor’s holiness. Another word for this is “co-suffering,” that is, bearing each other’s crosses as best we can, resisting the despairing nothingness that evil wants to draw us backward into.

The Boughton family is described with words like “probity.” This stuck out to me in my several heart-aching reads (my heart literally hurts); it means confirmed integrity, honesty, and comes from the Latin probitās (honesty), from probus (virtuous). Jack is not historically honest. Most people in his world don’t think he is virtuous. Even his godfather, John Ames, struggles to be hospitable toward him. Jack has an interest in how things break; he finds himself unable not to cause harm. But Robinson and Glory know that he has a particular kind of integrity and honesty, and his desire toward virtue is tortured by the difficulty he has in doing it. He struggles to understand his father’s theology and the teaching of the church, but still in middle age he is sincerely pursuing virtue in a culture steeped in the hypocrisy of racial sin, with all its webs and histories that have come home to Jack in the family he is unsuccessfully trying to build.

What happens in Home puts a stone upon my chest. Glory, herself wounded and struggling to find herself back at home, strains to see Jack and offers him intelligent companionship that is at once compassionate and restrained, concerned for his dignity and embracing. She pauses often, hesitates as it were, at the threshold between them. She has immense regard for him; indeed, she is the third person limited omniscient narrator of the book—everything true known about Jack comes from her perceptive gaze. I can open any page and find something remarkable she has observed or pretended not to see for his benefit. Here is one from Home (page 181):

The brightness in his face meant anxiety. When he was anxious a strange honesty overtook him. He did understandable things for understandable reasons, answering expectation in terms that were startlingly literal, as if in him the skeletal machinery of conventional behavior, the extension and contraction of the pulleys of muscle and sinew, was all exposed. And he was aware of this, embarrassed by it, inclined to pass it off, if he could, as irony, to the irritation of acquaintances and strangers, and she could only imagine, employers and police.

Note her perceptive concentration toward him and understanding that he struggles in this situation (and others) to function while bearing the weight of himself. She responds lightly, giving him a small job to do in the moment so that he can forget himself a little; she sees how the guests respond to him and knows the history; she encourages him but is aware that he is so often misunderstood and she cannot cure this trouble. These two have six siblings who are hale and successful. One is a doctor (Teddy, who always gets to offer saving help to people in the story and the family). Ames calls the siblings “estimable.” Do you hear the tacit references to one of the wounds of family? We don’t all land in the same place, or sometimes all of us land in the same place except one. Sometimes the very culture of a family that is good has difficulty making place for the stranger born in its midst. There is nothing malicious about this, but it imposes burdens.

In our imperfect hunger and thirst after righteousness, for ourselves and for others, there are often unintended consequences even when we succeed. In one passage Glory is described as having kept the habits of her pious youth that include reading the Bible morning and evening, but added to this routine is a disposition of fealty (Home, 101):

Like most of their obligations and many of their pleasures, this [referring to reading aloud from Scripture when they were together] was meant to please their father, to assure him that they loved the old life, that they had received all the good he had intended for them. To please him was so potent a motive that it displaced motives of their own, which no doubt would have included piety.

What a gift for a child and then a grown woman to have this virtuous habit, and, in the story, we feel the way Scripture deeply shapes her imagination and her inclination toward her brother and everyone else. Yet we also register the accretions of the will of another and the difficulty in orienting toward the proper object of affection (ordo amoris). In this passage Glory passes through such rich and profound content and Robinson shows a character with remarkable mental furniture and the muscle to move it. She’d dreamed of three children and a home of her own: “very different from this good and blessed and fustian and oppressive tabernacle of Boughton probity and kind intent” (Home, 102). Here Robinson tells us about the burdens of piety as well as those of prodigality that Jack carries. But none of these characters are simple enough to assign to a category or forget; they take a place in the reader’s mental living room because of their dense texture and reality. In dialogue with the literary inheritance of the nostos, Robinson adds a layer of Christian civilization to the Greek and Roman ones (Home, 102):

All bread is the bread of heaven, her father used to say. It expresses the will of God to sustain us in this flesh, in this life. Weary or bitter or bewildered as we may be, God is faithful. He lets us wander so we will know what it means to come home.

This passage is one-third of the way through this second book in the tetralogy. We don’t just need to get to the shore of Ithaka or the bed of Penelope, we need to come home to ourselves. We aren’t “right with [ourselves]” as Boughton says of Jack to his friend John. At the same time these old friends believe that in eternity this world will be Troy and “all that has passed here will be the epic of the universe, the ballad they sang in the streets. Because I don’t imagine any reality putting this one in the shade entirely, and I think piety forbids me to try” (Gilead, 57). A remarkable reference to the Aeneid in just the way the early church fathers and mothers thought of it—a description of this life’s resemblance to and preparation for that one; a sense that all we do, all we subjugate to that higher purpose will be given back in the fullness of a true home in a magnificent empire in the eschaton. But in both passages, Robinson revises, as all canonical authors do (see George Steiner’s Real Presences), the ancient sense of the relationship between now and then. We taste the goodness of the Lord in the land of the living, but we are often strange to ourselves and to those who are our beloved. Natural daily bread, grown with the wheat cultivated out back, is both manna and eucharist, but it grows by sweat and with thorn. Both of these books show not only edifices being built on top of each other but, closer to the ground, the taming and cultivation of overgrown land into gardens by major characters— Glory, Jack, Lila. These three grow flowers and vegetables, pull weeds, and give love, food, and beauty by their effort. Nature and grace, creation and redeemed creation have a sacramental relationship to each other. We are constantly eating the bread of heaven, touched by the rain of baptism, and tasting of the goodness of our true and ultimate home. But, for now, the two dimensions inhere.

While my heart aches to read “what it means to come home,” I do love this writer and intellectual friend for understanding the complexity of our experience of home alongside its eventual wholeness. Jack for all his encumbrances intrigues Robinson. She shows us that even the most prodigal among us is vastly more than that profligacy. I haven’t done due diligence to prove his prodigality, but you will have to read the book: he is an alcoholic, he steals, he has a child out of wedlock that he leaves to poverty, etc. . . . but these are not the truest things about him (it feels wrong to even list these things so reductionistically).

He also loves virtue, is honest, is longing to be a good father and to bless his own father. I would go so far as to say he is full of virtue, or the longing for it, and suffers the lack of it. He wants to do no harm and he can’t achieve that. Yet Glory and Ames are both able to say to him at the close of these two books that he is a good man. And that child he had as a teenager with a poor country girl, the child who never had a name, loved the short life he gave her by his error. Robinson goes to lengths to show us the ordinary delight that comes to the child before she steps on a rusty nail and dies. And teenage Glory, a character who never does not love the good and always knows what is beautiful, holds precious that child’s being and presence in the world; still, despite this virtue and appreciation and fittedness for motherhood she herself will not have a child. We endure painful contradictions inside our homes, as good as they might be. The novel is the breakdown of the human, and the epic the raising of the hero, but here Robinson gives us the profoundly Christian heroism of home. In Robinson’s four-novel panorama and miniature, home is certainly broken in small and large ways, despite its visible provision, but it is also the site on which we might receive and carry each other’s burdens. It is the location of piercing and costly beatitude.

Boughton’s prodigal son has come home with good will, and his presence builds to a torturous scene where the old man, who has so faithfully cherished and extended grace to his beloved son, close to death, lacerates Jack by revealing the burden he has carried for him and its unendurable pain. He recounts Jack’s worst offenses and discloses that he sees Jack in the same light now as he did all those years ago, saying (Home, 295):

I thanked God for him every day of his life, no matter how much grief, how much sorrow—and at the end of it all there is only more grief, more sorrow, and his life will go on that way, no help for it now. You see something beautiful in a child, and you almost live for it, you feel as though you would die for it, but it isn’t yours to keep or to protect. And if the child becomes a man who has no respect for himself, it’s just destroyed till you can hardly remember what it was.

Boughton, who has endured courageously, here falls down in the most hurtful way. He is at death’s door, and he can’t sustain his labor of co-suffering. I hate to thrust upon you this passage and to leave you feeling the full flower of human and fatherly impotence. It is a terrifying and haunting caution to me that leads me into desperate prayer and will hopefully silence me when I ought to be silent. Glory’s blessed answer in this scene is to respond to her father by pointing out that Jack is here now, his life has been hard and sad, and he has come home. She bears none of the marks of the older brother; she is full of blessing.

The good news is that Home doesn’t end here. I don’t want to spoil it for you, but I will say that, like Alyosha’s kiss in response to Ivan’s railing against God (The Brothers Karamazov), Robinson produces a kiss for Jack and for the reader. Glory’s response to this nightmare is like a bee that finds the sweetness in Jack’s presence and life, and the moment she does genuinely find it (unlike Myshkin in The Idiot, who falsely imposes it with drastic consequences because he can’t bear to see the ugliness of life) is described as “that terrible shock of joy—no, worse than joy, peace—that floods in like blood pushing into a limb that has been starved of it, like wild rescue, painful and wonderful and humbling” (Home, 323). And John Ames, who is finally able to bless his son by grace (Jack) at the end of both Gilead and Home says it this way: “Wherever you turn your eyes the world can shine like transfiguration. You don’t have to bring a thing to it except a little willingness to see. Only, who could have the courage to see it?” (Gilead, 245). Glory and John Ames are constantly illuminating beauty so blinding to eyes and hearts, and insisting, by example, that our work is to honor it. The world is charged with glory, and the book Home is charged by Glory, who has demonstrated true sight that transfigures. The sight is filled full with antinomy—we see both the tragic and the transfigured next to each other, for now. But Greek nostos and kleos from Homer are converted into Christian homecoming and glory that assert “blessed are those who mourn, / for they shall be comforted. . . . blessed are those who hunger and thirst after righteousness, / for they shall be filled.”

For G.H. and A.H.

Christine Perrin is the poetry editor for FORMA (with Noah Perrin), she has taught at Messiah University for twenty years, and she wrote Bright Mirror and Art of Poetry

Zeno of Elea famously argues in Aristotle’s Physics, “That which is in locomotion must arrive at the half-way stage before it arrives at the goal.” But to reach that halfway point, one would first need to reach another point halfway to the first halfway point, and so on. Thus motion is impossible, because to move, one would need to travel an infinite number of distances, which cannot happen. Diogenes, as legend has it, refuted Zeno by standing up and walking across the room.

Each year, when I introduced my physics students to Zeno’s claim, someone recreated Diogenes’s argument. Zeno’s argument that motion is impossible seems quaint, silly almost. But he made it in support of his teacher Parmenides’ idea that all is one: he was a philosophical monist. In this context, Zeno points out a genuine philosophical difficulty with the idea of plurality, articulating a tension we call the problem of the one and the many.

The Greeks understood two modes of plurality: quantity and size. We’ll call them the discrete and the continuous. The discrete is that which is countable; the continuous, that which has size but is not countable. For example, if I have some apples, I can count them and report that I have five apples. If I have some water, however, it would sound peculiar to count the water and say that I have seven waters. In fact, the distinction between countable and uncountable is woven into our very language. We use “fewer” for things that are countable and “less” for things that are not countable. You can’t say “I am fewer tall than she is” because height is a continuous length and not the result of counting. People who know how tall they are will raise an eyebrow at this!

So Zeno’s paradox, then, is this: if space is continuous and unendingly divisible then there is no smallest distance. Whatever distance I mark out, I can cut it in half and make a smaller distance. But particular distances are countable things. So in any finite (continuous) distance, there are infinitely many (very small!) discrete countable distances. How can that be? How can something be both countable and uncountable at once?

What Zeno saw as a paradox that rendered the idea of plurality incoherent, we can see as an important philosophical and mathematical insight: there is a relationship between the discrete and continuous that is both subtle and important.

We have gradually obscured that relationship over the last two thousand years. At times one waxes while the other wanes; the one is subsumed into the other. We resolve Zeno’s paradoxes, but rarely do we carefully preserve the ancient distinction between the countable and that which has size, the discrete and continuous. This is, I think, to our detriment. If we preserve the distinction that Zeno saw, we will find it a profoundly creative tension that illuminates much of how we share mathematics with young people.

Two Modes of Quantity

Arithmetic begins Greek mathematics, and likewise our curricula. It takes its name from the word arithmos, which Jacob Klein notes “indicates in each case a definite number of definite things.”1 That is, an arithmos is the result of counting: it names a discrete number of things. For the first few years of school, we use a definition of number that makes intuitive sense and follows the ancient witness. Euclid says in the opening of book 7 that number is “a multitude composed of units.” From that definition he builds ideas like primality, coprimality, and a theory of ratios and proportions.

1. Klein, Greek Mathematical Thought and the Origin of Algebra.

Geometry, the study of continuous magnitude, is the second lung of Greek mathematics. Euclid begins his treatise with definitions: a point is “that which has no part,” and a line is a “breadthless length.” In his geometry, Euclid is not interested in a line whose length is five or an angle of thirty degrees. Rather, he is interested in the relationships between continuous lines that we can understand without discrete measurements of their length or angles.

In modern mathematical education, we have collapsed the two modes of quantity into one another. Many modern textbooks trumpet “integrated” geometry and algebra. We teach young children the number line—an artifact of a nineteenth-century attempt to make arithmetic more rigorous—that blurs the distinction between discrete number and continuous line. The ruler and protractor, wholly absent from Euclid, invade our angles and lengths and fuse the continuous geometry of shape with the discrete counting of arithmetic. We call things like √2 numbers without exposing students to the necessarily geometrical meaning of that idea: it comes from the length of the diagonal of a square whose sides are 1. Whatever √2 is, it’s not the result of counting anything!2

We teach division several times. For example, consider the division 13 divided by 3. The first answer that a student might learn is 4 remainder 1. We could imagine a picture with dots, where we have four rows of three dots, and one left over. The next answer children might be taught is 13.333333 . . ., which is a very different sort of answer. Here we’ve taken the same question and treated it once as a part of arithmetic, with a discrete answer, and again almost as part of geometry with an answer that is not the result of counting. But the language we use to describe the division is exactly the same because we omit the clear conceptual categories the Greeks used. No wonder students struggle.

2. If we wanted to think about √2 as a multitude composed of units, we’ll discover something amazing: the units that measure the diagonal of a square are incommensurable with the units that measure the side of the square. This was so shocking to the Pythagoreans that they (legendarily) murdered the man who discovered it.

A Creative Tension

Some mathematical problems are unexpectedly difficult for seventh graders. Consider the equation

2x+4=8. Essentially every seventh grader can make sense of that, and rightly say that it is true when x=2. But when asked to make sense of the equation

2x+5=8, things get murky for many students. Some (rightly) say that the equation is true when x=3/2. Others say that the equation has no solutions or that they’re not sure how to solve it. Still others offer numerically puzzling answers. But the two equations I’ve just offered are algebraically identical. The sequence of algebraic steps to solve them is the same: subtract a number from both sides of the equation and then divide both sides of the equation by the same thing. Why is one harder than the other? The easy one lives squarely in the discrete world of arithmetic. The hard one does not.

We further muddy the waters for our students with word problems like this:

Each table in a classroom can accommodate two students. There are eight students in the class, but five of them are sitting in a circle on the floor. How many tables does the classroom need to accommodate the remaining students?

We might want our students to represent that situation as an algebraic equation, which would be 2x+5=8. But the solution isn’t 3/2 tables (which doesn’t make sense), but 2 tables. Students must intuit that this story lives in the world of arithmetic, and the unit is the table, and that the algebraic equation only approximately models the situation. That’s a lot to ask of a seventh grader without offering them the conceptual categories of the discrete and continuous to shape their understanding.

So collapsing the creative tension between discrete number and continuous magnitude adds accidental complexity and confusion to the mathematical work we ask of students at a critical juncture in their educational lives.

Harmonious Flow

Let’s look back to Euclid’s definition of number: “a multitude composed of units.” We focused earlier on the idea of a “multitude,” but now let’s think a bit about “units.” That’s a word we’ve all encountered: units are the things teachers intermittently take off points for omitting in science classes. What are they doing in Euclid’s definition of number?

From the Latin, a “unit” is a oneness, a principle of unity. To count something, we must first choose a principle of unity to count by (apples, or people, or trees, or pure monads). Choosing a unit allows us to take something continuous and uncountable (like the amount of water in a bucket) and make it countable. We choose ounces, and then we can count 145 ounces of water in the bucket. We choose inches, and then we can count 72 inches in my height. We could choose feet and we count a different number of feet in my height! That conversion of the continuous into the discrete—which we call “measurement”—beats at the heart of the natural sciences. Claudius Ptolemy carefully measured the position of the stars using a circular bronze disc with degrees marked out on it as the unit. Galileo measured the passage of time using his pulse as the unit. The kilogram sat in Paris. Fabulously expensive clocks use the radioactive decay events of cesium as the unit. Even the humble ruler takes continuous length and makes it discrete.

So we have a harmonious flow from the continuous that we perceive in the world to the countable discrete. If we lack the conceptual categories of discrete and continuous, how can we sensibly talk to our students about the meaning of measurement in the sciences? I’d submit that we can’t.

Does that flow operate in reverse, though? Does it move from the discrete to the continuous? It does!3 Imagine that you are Robert Boyle and want to uncover the relationship between the pressure exerted by a gas and its volume. You might measure the volume of gas to be 100 liters and the pressure it exerts to be 5 inches of mercury. You might take another measurement, say a volume of 50 liters and a pressure of 10 inches of mercury. From repeated discrete observations of that sort, you might intuit the harmony you seek: that the pressure is inversely proportional to the volume, P 1/V. Discovering that continuous harmony, though, comes from examining particular discrete measurements. So just as measuring moves from the continuous to the discrete, there is a synthesis that moves from the discrete to the continuous.

We ask our students to do this in all sorts of physics and chemistry lab work. How much easier for students to understand the meaning of lab work if they see it as a process of choosing units to make continuous quantities countable, counting those discrete quantities, and then synthesizing the discrete to return to a continuous harmony!

Mathematics and Theology

The joys and benefits of preserving the creative tension between the discrete and continuous extend beyond mathematics and the natural sciences. After all, we began with a philosophical problem. Perhaps this tension can speak into students’ understanding of philosophy and theology. What would it look like to talk to students about the triune nature of God if they were prepared by studying the tension between the one and the many? The number three is both a unity and a plurality. Indeed, the proper preservation of the creative tensions in mathematics will bear wonderful fruit for students across their intellectual lives.

William Carey studied classics and history at the University of Virginia before teaching Latin, mathematics, and science at a classical Christian school in Virginia. His current project is bringing his love for the classics and mathematics together to build a classical mathematics curriculum. He and his wife, Maren, are members of Shepherd of the Hills Lutheran Church in Haymarket, Virginia.

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3. I’m deeply indebted here to Ravi Jain’s thought and his work in the forthcoming Enchanted Cosmos.